Local Hermite (LH) Method: An accurate and robust smooth technique for high-gradient strain reconstruction in digital image correlation

High-gradient strain field (HSF) measurement is attracting more and more attention from engineering and scientific fields, where digital image correlation (DIC) is widely adopted to calculate the dramatically changing displacement fields on stressed samples. Accurate reconstruction of reliable strain field from noisy displacement field is one of the key issues, since strain calculation is highly sensitive to displacement noise. The formally proposed improved Hermite finite element smoothing method (IHFESM) and fast Hermite element method (FHEM) are effective global smoothing techniques based on Tikhonov regularization. However, they involve complex meshing and global regularization matrix assembly processes. In this work, we present a local version of FHEM, called local Hermite (LH) method, in which one Hermite element is taken as a smoothing window centered on one displacement data, and the whole field is handled point-wisely. Two types of LH method are obtained by employing Hermite element with two types of continuities, i.e. C-1 and C-2. The smoothed displacement and strain are consequently computed from the regularized local surface as done in FHEM. Two kinds of simulated noisy displacement fields and one high-gradient displacement field obtained from shape memory alloy (SMA) tensile test are used to compare the performance of the proposed LH methods with the widely used point-wise least squares (PLS) method. Experiments show that LH method with C-2 element is nearly insensitive to window size, which is a quite useful property for practical engineering test without much prior knowledge. More importantly, it generally produces lower error than PLS in resolving local HSF. Thus, LH is a robust and accurate method which is highly recommended for practical HSF measurement.